Search results
Results From The WOW.Com Content Network
In other words, a problem with input size n is in NC if there exist constants c and k such that it can be solved in time O((log n) c) using O(n k) parallel processors. Stephen Cook [ 1 ] [ 2 ] coined the name "Nick's class" after Nick Pippenger , who had done extensive research [ 3 ] on circuits with polylogarithmic depth and polynomial size.
Using little omega notation, it is ω(n c) time for all constants c, where n is the input parameter, typically the number of bits in the input. For example, an algorithm that runs for 2 n steps on an input of size n requires superpolynomial time (more specifically, exponential time).
For example, in the search path for a string of length k, there will be k traversals down middle children in the tree, as well as a logarithmic number of traversals down left and right children in the tree. Thus, in a ternary search tree on a small number of very large strings the lengths of the strings can dominate the runtime.
L further relates to the class NC in the following way: NC 1 ⊆ L ⊆ NL ⊆ NC 2. In words, given a parallel computer C with a polynomial number O ( n k ) of processors for some constant k , any problem that can be solved on C in O (log n ) time is in L , and any problem in L can be solved in O (log 2 n ) time on C .
The analysis of the former and the latter algorithm shows that it takes at most log 2 n and n check steps, respectively, for a list of size n. In the depicted example list of size 33, searching for "Morin, Arthur" takes 5 and 28 steps with binary (shown in cyan) and linear (magenta) search, respectively.
A single-tape deterministic Turing machine can solve the problem, for n elements of m ≥ log n bits each, in time O(n 2 m(m+2–log n)), while on a nondeterministic machine the time complexity is O(nm(n + log m)). [6]
To show that NL is contained in C, we simply take an NL algorithm and choose a random computation path of length n, and execute this 2 n times. Because no computation path exceeds length n, and because there are 2 n computation paths in all, we have a good chance of hitting the accepting one (bounded below by a constant).
Created independently in 1977 by W. Eddy and in 1978 by A. Bykat. Just like the quicksort algorithm, it has the expected time complexity of O(n log n), but may degenerate to O(n 2) in the worst case. Divide and conquer, a.k.a. merge hull — O(n log n) Another O(n log n) algorithm, published in 1977 by Preparata and Hong. This algorithm is also ...